For one thing, a "tax district" like what is described here is aimed at addressing a particular challenge in certain tax structures, where the major sources of taxation (corporate, personal income, etc.) don't raise revenue from businesses that use public resources but may not pay the cost of them. This "tax district" approach is ideally suited to pay for infrastructure improvements like transportation, water and sewer utilities in industries that employ a lot of people but don't contribute enough to the tax base to cover the cost of their burden on the local infrastructure.
If I live in City A and work in City B, one of the anomalies of the tax system may be that I pay all of my municipal taxes to City A but spend a third of my life in City B.
In Ohio both the cities can charge income tax. In most cases City A will count the tax you pay to City B as a credit. I live in a city with 2.25% tax and work in a city with a 1.5% tax, so I pay 1.5% to City B and a net of 0.75% to City A. However, the residential city is not required to credit the tax paid in the working city. If those cities were reversed I would have to pay 2.25% to the city I worked in and 0.5% more to my residential city because they only allow a maximum credit of 1.0% instead of the full amount.
Taxation without representation is alive and well in Ohio.